Skip to main content

Generalized F-iterated function systems on product of metric spaces

Journal of Fixed Point Theory and Applications volume 17, pages 575–595 (2015)Cite this article

Abstract

In this paper, we start from an F-contraction defined on a metric space X into itself, introduced by Wardowski [Fixed Point Theory Appl. 2012 (2012), doi:10.1186/1687-1812-2012-94], and extend it to the case of mappings defined on the space X I into X endowed with the supremum metric, where I is a set of positive integers. Next, we consider the generalized iterated function systems composed of F-contractions on X I improving some fixed point results from the classical Hutchinson–Barnsley theory of iterated function systems. Some illustrative examples are given.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. M. F. Barnsley, Fractals Everywhere. 2nd ed., Academic Press Professional, Boston, MA, 1993.

  2. Barnsley M. F., Vince A.: Real projective iterated function systems. J. Geom. Anal. 22, 1137–1172 (2012)

    MATH  MathSciNet  Article  Google Scholar 

  3. V. Berinde, Iterative Approximation of Fixed Points. Lecture Notes in Math., Springer, Berlin, 2007.

  4. D. Dumitru, Generalized iterated function systems containing Meir-Keeler functions. An. Univ. Bucureşti Mat. 58 (2009), 109–121.

  5. Fernau H.: Infinite iterated function systems. Math. Nachr. 170, 79–91 (1994)

    MATH  MathSciNet  Article  Google Scholar 

  6. J. Hutchinson, Fractals and self-similarity. Indiana Univ. Math. J. 30 (1981), 713–747.

  7. K. Leśniak, Infinite iterated function systems: A multivalued approach. Bull. Pol. Acad. Sci. Math. 52 (2004), 1–8.

  8. E. Llorens-Fuster, A. Petruşel and J.-C. Yao, Iterated function systems and well-posedness. Chaos Solitons Fractals 41 (2009), 1561–1568.

  9. R. Miculescu, Generalized iterated function systems with place dependent probabilities. Acta Appl. Math. 130 (2014), 135–150.

  10. A. Mihail, Recurrent iterated functions systems. Rev. Roumaine Math. Pures Appl. 53 (2008), 43–53.

  11. A. Mihail and R. Miculescu, Applications of fixed point theorems in the theory of generalized IFS. Fixed Point Theory Appl. 2008 (2008), doi:10.1155/2008/312876.

  12. A. Mihail and R. Miculescu, Generalized IFSs on noncompact spaces. Fixed Point Theory Appl. 2010 (2010), doi:10.1155/2010/584215.

  13. N.-A. Secelean, Countable Iterated Function Systems. Lambert Academic Publishing, 2013.

  14. N.-A. Secelean, Generalized countable iterated function systems. Filomat 25 (2011), 21–36.

  15. N.-A. Secelean, Generalized iterated function systems on the space l ∞(X). J. Math. Anal. Appl. 410 (2014), 847–858.

  16. N.-A. Secelean, Iterated function systems consisting of F-contractions. Fixed Point Theory Appl. 2013 (2013), doi:10.1186/1687-1812-2013-277.

  17. N.-A. Secelean, The existence of the attractor of countable iterated function systems. Mediterr. J. Math. 9 (2012), 61–79.

  18. F. Strobin and J. Swaczyna, On a certain generalisation of the iterated function system. Bull. Aust. Math. Soc. 87 (2013), 37–54.

  19. Vince A.: Möbius iterated function systems. Trans. Amer. Math. Soc. 365, 491–509 (2013)

    MATH  MathSciNet  Article  Google Scholar 

  20. D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012 (2012), doi:10.1186/1687-1812- 2012-94.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, Lucian Blaga University of Sibiu, Sibiu, Romania

    Nicolae-Adrian Secelean

Authors
  1. Nicolae-Adrian Secelean
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicolae-Adrian Secelean.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Secelean, NA. Generalized F-iterated function systems on product of metric spaces. J. Fixed Point Theory Appl. 17, 575–595 (2015). https://doi.org/10.1007/s11784-015-0235-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11784-015-0235-2

Mathematics Subject Classification

  • Primary 28A80
  • Secondary 47H10
  • 54E50

Keywords

  • F-contraction
  • generalized F-contraction
  • generalized iterated function system
  • attractor
  • Hausdorff–Pompeiu metric
  • fixed point